Visitors Talk : Optimal Dimensionality Sampling and Spatially Localized Analysis on the Sphere for Diffusion MRI Applications

Dr. Zubair Khalid is an Associate Professor in the Electrical Engineering Department, School of Science and Engineering, Lahore University of Management Sciences. He received Ph.D. degree from the Australian National University funded by the prestigious Endeavour Scholarship. His research interests include the use of machine learning, data processing, computer vision, natural language processing and the development of novel information processing techniques in these areas for applications in cosmology, medical imaging, acoustics, speech processing and data-driven urban development. He has supervised 7 Ph.D. students and has over 80 publications to date in refereed international journals and conferences. He is a senior member of IEEE and is serving on the Editorial Board as an Associate Editor for the IEEE Signal Processing Letters. More details regarding his academic profile and his centre are available at www.zubairkhalid.org and http://city.lums.edu.pk/  

Slepian functions for capturing the spatially localized information of the MRI data

Signals on the sphere are encountered in many areas of science and engineering such as medical imaging, computer graphics, acoustics, planetary sciences, geophysics, cosmology, quantum mechanics, wireless communication, and antenna design. To analyze the spatially localized information in these applications, I will present a method called spatial-Slepian transform (SST). This method uses special functions called Slepian functions, limited in frequency and optimally concentrated in space, for capturing the spatially localized information of the data. I will also demonstrate how the SST can be used to detect localized variations in the data.

I will also present a sampling scheme on the sphere for the reconstruction of the diffusion signal in dMRI from an optimal number of measurements, and an associated spherical harmonic transform (SHT) that ensures the rotationally invariant reconstruction accuracy on the order of numerical precision for band-limits of interest in dMRI.